A population-level analysis is proposed to address data sparsity when building predictive models for engineering infrastructure. Utilizing an interpretable hierarchical Bayesian approach and operational fleet data, domain expertise is naturally encoded (and appropriately shared) between different subgroups, representing (1) use-type, (2) component, or (3) operating condition. Specifically, domain expertise is exploited to constrain the model via assumptions (and prior distributions) allowing the methodology to automatically share information between similar assets, improving the survival analysis of a truck fleet (15% and 13% increases in predictive log-likelihood of hazard) and power prediction in a wind farm (up to 82% reduction in the standard deviation of maximum output prediction). In each asset management example, a set of correlated functions is learnt over the fleet, in a combined inference, to learn a population model. Parameter estimation is improved when subfleets are allowed to share correlated information at different levels in the hierarchy; the (averaged) reduction in standard deviation for interpretable parameters in the survival analysis is 70%, alongside 32% in wind farm power models. In turn, groups with incomplete data automatically borrow statistical strength from those that are data-rich. The statistical correlations enable knowledge transfer via Bayesian transfer learning, and the correlations can be inspected to inform which assets share information for which effect (i.e., parameter). Successes in both case studies demonstrate the wide applicability in practical infrastructure monitoring, since the approach is naturally adapted between interpretable fleet models of different in situ examples.